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MIT OpenCourseWareMIT 18.06 Linear Algebra, Spring 2005 (2005)

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*Please note that Lecture 4 is unavailable in a higher quality format.

Instructor/speaker: Prof. Gilbert Strang
View the complete course at: http://ocw.mit.edu/18-06S05

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu


This movie is part of the collection: MIT OpenCourseWare

Producer: MIT OpenCourseWare
Audio/Visual: sound, color
Keywords: systems of equations, vector spaces, positive definite matrices, matrix theory, linear algebra, determinants, eigenvalues, similarity, least-squares approximations, stability of differential equations, networks, Fourier transforms, Markov processes

Creative Commons license: Attribution-Noncommercial-Share Alike 3.0 United States


Individual Files

Movie Files MPEG4 Ogg Video
Lecture 1: The geometry of linear equations 88.9 MB 
172.7 MB 
Lecture 2: Elimination with matrices 101.7 MB 
193.8 MB 
Lecture 3: Multiplication and inverse matrices 104.7 MB 
200.2 MB 
Lecture 4: Factorization into A = LU 104.0 MB 
201.5 MB 
Lecture 5: Transposes, permutations, spaces R^n 101.8 MB 
194.0 MB 
Lecture 6: Column space and nullspace 102.8 MB 
197.9 MB 
Lecture 7: Solving Ax = 0: pivot variables, special solutions 93.1 MB 
179.1 MB 
Lecture 8: Solving Ax = b: row reduced form R 101.2 MB 
190.9 MB 
Lecture 9: Independence, basis, and dimension 107.9 MB 
199.8 MB 
Lecture 10: The four fundamental subspaces 106.1 MB 
190.6 MB 
Lecture 11: Matrix spaces; rank 1; small world graphs 102.6 MB 
193.4 MB 
Lecture 12: Graphs, networks, incidence matrices 102.2 MB 
197.5 MB 
Lecture 13: Quiz 1 review 101.3 MB 
188.8 MB 
Lecture 14: Orthogonal vectors and subspaces 105.5 MB 
202.8 MB 
Lecture 15: Projections onto subspaces 103.1 MB 
187.3 MB 
Lecture 16: Projection matrices and least squares 102.9 MB 
195.7 MB 
Lecture 17: Orthogonal matrices and Gram-Schmidt 108.1 MB 
203.4 MB 
Lecture 18: Properties of determinants 104.1 MB 
198.1 MB 
Lecture 19: Determinant formulas and cofactors 113.5 MB 
219.3 MB 
Lecture 20: Cramer's rule, inverse matrix, and volume 110.1 MB 
211.5 MB 
Lecture 21: Eigenvalues and eigenvectors 115.0 MB 
210.2 MB 
Lecture 22: Diagonalization and powers of A 110.2 MB 
210.1 MB 
Lecture 23: Differential equations and exp(At) 114.0 MB 
219.7 MB 
Lecture 24: Markov matrices; fourier series 114.3 MB 
220.5 MB 
Lecture 24b: Quiz 2 review 107.9 MB 
202.5 MB 
Lecture 25: Symmetric matrices and positive definiteness 98.0 MB 
183.3 MB 
Lecture 26: Complex matrices; fast fourier transform 102.2 MB 
185.6 MB 
Lecture 27: Positive definite matrices and minima 108.3 MB 
205.5 MB 
Lecture 28: Similar matrices and jordan form 102.6 MB 
189.1 MB 
Lecture 29: Singular value decomposition 92.8 MB 
171.6 MB 
Lecture 30: Linear transformations and their matrices 105.7 MB 
200.4 MB 
Lecture 31: Change of basis; image compression 112.1 MB 
217.4 MB 
Lecture 32: Quiz 3 review 100.7 MB 
193.2 MB 
Lecture 33: Left and right inverses; pseudoinverse 90.1 MB 
170.8 MB 
Lecture 34: Final course review 92.9 MB 
173.8 MB 
Image Files Animated GIF Thumbnail
Lecture 1: The geometry of linear equations 443.4 KB 
5.8 KB 
Lecture 2: Elimination with matrices 441.7 KB 
6.5 KB 
Lecture 3: Multiplication and inverse matrices 429.2 KB 
5.7 KB 
Lecture 4: Factorization into A = LU 436.9 KB 
5.5 KB 
Lecture 5: Transposes, permutations, spaces R^n 428.9 KB 
5.5 KB 
Lecture 6: Column space and nullspace 446.3 KB 
6.2 KB 
Lecture 7: Solving Ax = 0: pivot variables, special solutions 437.2 KB 
5.0 KB 
Lecture 8: Solving Ax = b: row reduced form R 440.1 KB 
5.1 KB 
Lecture 9: Independence, basis, and dimension 437.6 KB 
5.9 KB 
Lecture 10: The four fundamental subspaces 439.5 KB 
5.1 KB 
Lecture 11: Matrix spaces; rank 1; small world graphs 429.3 KB 
5.5 KB 
Lecture 12: Graphs, networks, incidence matrices 436.7 KB 
5.2 KB 
Lecture 13: Quiz 1 review 416.7 KB 
4.9 KB 
Lecture 14: Orthogonal vectors and subspaces 437.0 KB 
7.6 KB 
Lecture 15: Projections onto subspaces 423.9 KB 
5.9 KB 
Lecture 16: Projection matrices and least squares 439.7 KB 
6.1 KB 
Lecture 17: Orthogonal matrices and Gram-Schmidt 437.8 KB 
5.5 KB 
Lecture 18: Properties of determinants 423.9 KB 
5.2 KB 
Lecture 19: Determinant formulas and cofactors 452.3 KB 
7.3 KB 
Lecture 20: Cramer's rule, inverse matrix, and volume 440.5 KB 
6.4 KB 
Lecture 21: Eigenvalues and eigenvectors 433.0 KB 
6.3 KB 
Lecture 22: Diagonalization and powers of A 440.1 KB 
6.3 KB 
Lecture 23: Differential equations and exp(At) 429.1 KB 
5.7 KB 
Lecture 24: Markov matrices; fourier series 436.9 KB 
6.5 KB 
Lecture 24b: Quiz 2 review 432.1 KB 
4.9 KB 
Lecture 25: Symmetric matrices and positive definiteness 422.9 KB 
5.6 KB 
Lecture 26: Complex matrices; fast fourier transform 422.6 KB 
5.6 KB 
Lecture 27: Positive definite matrices and minima 441.5 KB 
6.6 KB 
Lecture 28: Similar matrices and jordan form 446.6 KB 
5.8 KB 
Lecture 29: Singular value decomposition 408.7 KB 
6.7 KB 
Lecture 30: Linear transformations and their matrices 433.9 KB 
6.0 KB 
Lecture 31: Change of basis; image compression 438.2 KB 
6.5 KB 
Lecture 32: Quiz 3 review 436.1 KB 
7.3 KB 
Lecture 33: Left and right inverses; pseudoinverse 448.7 KB 
6.9 KB 
Lecture 34: Final course review 433.4 KB 
6.4 KB 
Information FormatSize
MIT18.06S05_MP4_files.xml Metadata [file] 
MIT18.06S05_MP4_meta.xml Metadata 1.4 KB 
MIT18.06S05_MP4_reviews.xml Metadata 1.3 KB 

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Average Rating: 3.50 out of 5 stars3.50 out of 5 stars3.50 out of 5 stars3.50 out of 5 stars

Reviewer: sandipb - 3.00 out of 5 stars3.00 out of 5 stars3.00 out of 5 stars - March 1, 2012
Subject: Lower quality than youtube
I downloaded both the mp4 versions here and compared it with the mp4 version downloadable from youtube for the same courses. The quality in youtube seemed markedly better. I agree with the other reviewer though - the smaller mp4 files are of much better quality than the larger one here. The youtube mp4s are only slightly larger than the _512.mp4 files here.

Reviewer: daflory - 4.00 out of 5 stars4.00 out of 5 stars4.00 out of 5 stars4.00 out of 5 stars - June 14, 2011
Subject: Technical comments
Be sure to download the MPEG4 version if possible.

Both the OGV and the MP4 (AVC) look terrible (blocky and jittery), as if they were re-encoded from a bad source.

The MPEG4 version is not only the smallest, but is far easier to watch. The writing on the blackboard is easy to read.